3 The diagram shows a sketch of a curve and a line.
\includegraphics[max width=\textwidth, alt={}, center]{c7f38f7e-75aa-4b41-96fd-f38f968c225c-06_520_588_351_742} The curve has equation \(y = x ^ { 4 } + 3 x ^ { 2 } + 2\). The points \(A ( - 1,6 )\) and \(B ( 2,30 )\) lie on the curve.

1. Find an equation of the tangent to the curve at the point \(A\).
2. 1. Find \(\int _ { - 1 } ^ { 2 } \left( x ^ { 4 } + 3 x ^ { 2 } + 2 \right) \mathrm { d } x\).
   2. Calculate the area of the shaded region bounded by the curve and the line \(A B\).
      [0pt] [3 marks] \(4 \quad\) A circle with centre \(C\) has equation \(x ^ { 2 } + y ^ { 2 } + 2 x - 6 y - 40 = 0\).